Kakuro: rules, strategy, and free play
Kakuro is a number-crossword puzzle. Fill the white cells with digits 1–9 so each horizontal or vertical run of cells sums to the clue shown in the adjacent black cell. No digit may repeat within a single run.
THE RULES
- Fill every white cell with a digit from 1 to 9 (no zeros).
- Each run (consecutive white cells in a row or column) must sum to the clue in the adjacent black cell.
- No digit repeats within a single run. A run of three cells summing to 7 must therefore be a unique combination — 1+2+4 — since 1+3+3 is illegal.
BEGINNER STRATEGY
- Use forced combinations. Some clue + run-length pairs only have one possible digit set: a 2-cell run summing to 3 can only be {1, 2}, a 2-cell summing to 17 only {8, 9}, and so on. Memorising these 'magic' combos unlocks fast deductions.
- Cross-reference rows and columns. Every cell participates in two runs (one row, one column). The digit you place must satisfy both runs simultaneously. The intersection of 'allowed-by-row' and 'allowed-by-column' candidates is usually a single digit when both runs are short.
- Eliminate impossible digits early. A 3-cell run summing to 6 forces the digit set {1, 2, 3} — so a 7, 8, or 9 anywhere in that run is impossible. Mark candidates out before placing concrete values.
- Never guess. Like Sudoku, a legitimate Kakuro has exactly one valid solution that can be found by deduction. If you find yourself guessing, back up and look for a run-length / clue pair you missed.
COMMON MISTAKES
- Forgetting the no-repeat rule. A 3-cell run summing to 6 is NOT {1, 2, 3} OR {2, 2, 2}. Digits cannot repeat within a run. {2, 2, 2} is illegal regardless of the sum. Always verify that your candidate set uses distinct digits.
- Ignoring the column run while filling the row. Every cell belongs to two runs at once. Placing a digit that satisfies the row run but conflicts with the column run is an error. Always check both directions before committing.
- Not using forced combinations first. Some clue + length pairs have only one possible digit set (e.g. 3 cells summing to 7 must be {1, 2, 4}). Identify these early — they constrain the whole grid before you've placed a single digit.
- Treating long runs as flexible. A long run (5+ cells) feels like it has many options. But combined with its clue and the digits already forced by crossing runs, the real candidate set is often smaller than it looks. Pencil-mark every long run before placing anything in it.
HOW TO THINK ABOUT IT
Kakuro is a constraint-intersection puzzle. Each cell sits at the crossing of two runs. Your goal is to find cells where the 'digits allowed by the row run' and the 'digits allowed by the column run' overlap in exactly one value. Forced combinations are your primary tool — not arithmetic, but recognition. The more digit-set patterns you internalize, the faster the intersections resolve themselves.
WHY THIS PUZZLE REWARDS YOU
Kakuro grids are smaller than Sudoku (typically 5×5 to 10×10) but the deductions are deeper. Where Sudoku rewards quick scanning, Kakuro rewards arithmetic intuition — recognising which sums force a unique digit set, which intersections lock a cell to one value, and when a long run can't possibly use a specific digit. Players who enjoy crosswords and Killer Sudoku usually love Kakuro too.
VARIANTS
- Killer Sudoku. Cage sums inside a 9×9 Sudoku grid. The cage constraint is Kakuro-like — digits in a cage must sum to the target without repeating — but you're also bound by Sudoku's row, column, and box rules.
- Sumplete. A lighter sum-matching puzzle: each cell is either kept or deleted, and the remaining digits in each row and column must hit their target sums. Simpler digit pool (no run-length constraint), but the deletion twist adds a new decision layer.
- Number Crossword. Across-only arithmetic expressions where each run evaluates to a multi-digit answer. Similar crossword layout, but clues are equations rather than sum targets.
YOU MIGHT ALSO LIKE
Killer Sudoku →
Sudoku rules + cage sums — the closest cousin to Kakuro.
Calcudoku →
Arithmetic cages, but with multiplication / division too.
Number Crossword →
Across-only arithmetic crossword — clues evaluate to multi-digit answers.
Sumplete →
Lighter sum-matching puzzle — same number-crossing feel.
Play today's Sudoku →
Free, no install — the classic 1–9 grid Kakuro borrows from.
Kakuro strategy for beginners →
Unique-sum runs, cross-referencing, the no-repeat eliminator.
Kakuro: how to think →
Magic-sum table + cross-referencing — the mindset shift.
Kakuro vs Sudoku →
Arithmetic-first vs logic-first — same digit range, different constraints.
Sumplete vs Kakuro →
The lighter arithmetic sibling — same sum targets, no combination enumeration.
Kakuro vs Killer Sudoku →
Both use cage sums — what changes when a Latin square enters the picture.
Number Crossword vs Kakuro →
Same crossword layout — what changes when clues are expressions, not digit sums.
Beginner mistakes in logic puzzles →
Common first-timer patterns that stall progress across all number puzzles.
READ MORE
How to solve Kakuro: a beginner's guide →
Kakuro looks like arithmetic. It isn't — it's a constraint puzzle. Forced combinations and the no-repeat rule unlock it.
Kakuro strategy: medium and hard techniques →
Combination narrowing, locked sets, and sum-region arithmetic — the tools that break hard Kakuro puzzles.
MORE NUMBER PUZZLES
Daily puzzle →
Today's free puzzle — same board for everyone.
Challenge a friend →
Same puzzle, head-to-head. Fastest wins.
Your ghost →
Grow your companion with every puzzle you solve.
PLAY IT IN GRIDJOY — FREE ON ANDROID
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